Thin film materials have been used in a wide variety of science and technology areas from computer chips and solar cells to wear-resistant coatings. However, it has been difficult to characterize the elastic properties of thin films with thicknesses in the nanometer range. In real-world applications, thin films are predominately attached to substrates. The mechanical properties of a composite thin film/substrate structure are typically dominated by the substrate due to its large thickness. According to Standard cantilever methods for characterization of elastic properties, resolution is lost, as the film thickness drops to the nano- and subnanometer range (see B. S. Berry et al., “Vibrating Reed Internal Friction Apparatus for Films and Foils”, IBM Journal of Research and Development (1975) vol. 19, p. 334; and K. E. Petersen et al., “Young's modulus measurements of thin films using micromechanics, Journal of Applied Physics, (1979) vol. 50, p. 6761). (Further, according to J. J. Vlassak and W. D. Nix, Journal of Materials Research, “A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films”, (1992), vol. 7, p. 3242): “Releasing the thin films from substrates and measuring the elastic properties of free standing films has been the primary solution to this loss of resolution”. In most circumstances, however, thin films are simply too fragile to withstand such experiments. In addition, there is no guarantee that the elastic properties would be the same for films on a substrate as for free standing films as the material properties of a thin film may often be sensitive to its interface.
There are two fundamental methods to measure the elastic moduli of a material: static and dynamic. In the static method, a local small stress is applied to the material and the corresponding strain is measured. Such measurements are typically inaccurate-often by a factor of 2 or more-because of contributions to the strain from material creep and local defects. More accurate modulus measurements are performed dynamically: by exciting the natural vibrations of a mechanical resonator made of the material in question (typically in the form of a beam) and by measuring its resonance frequencies. The accuracy of such measurements depends on the bandwidth of the resonator, which is directly related to the quality factor Q of the resonator as Δf=f0/Q, where f0 is the resonance frequency. The higher the Q is, the smaller the bandwidth will be, hence the higher the frequency resolution (lower Δf) of the resonator (see FIG. 8A and FIG. 8B, regarding variations of Q and frequency). According to L. Kiesewetter et al., “Determination of Young's moduli of micromechanical thin films using the resonance method” Sensors and Actuators A, 35 (1992) 153459, [by] using different excitation methods, including photothermal, acoustic and mechanical, the thin-beam resonating structures can be forced to vibrate. According D. F. McGuigan et al., “Measurements of the mechanical Q of single-crystal silicon at low temperatures”, Low Temperature Physics, (1978) vol. 30, p. 621: Although there are specifically designed mechanical resonators with quality factors (Q) of 108 to 109, they are all bulky and not suitable or thin film modulus measurements. According to G. J. McShane, et al., “Young's modulus measurement of thin film materials using micro-cantilevers”, Microengineering (2006) vol. 16, p. 1926: The thinnest cantilever-shaped resonators that are capable of carrying a thin film have a Q no larger than 106. As a result, the elastic properties of many thin film materials are either poorly characterized or not characterized at all. According to Y.-H. Huh et al., “Measurement Mechanical Properties of Thin Film by Membrane Deflection Test” Experimental Mechanics, (2010) vol. 50, p. 429 and further according to Y. Cao, et al., “Nanoindentation measurements of the mechanical properties of polycrystalline Au and Ag thin films on silicon substrates: Effects of grain size and film thickness” Materials Science Engineering (2006) vol. A, pp. 427, 232: The measured values of Young's moduli of some commonly used materials can differ by a factor of two or more, depending on how the measurements were carried out.
The key to obtaining a high Q mechanical resonator is twofold. First, the resonator has to be made from an intrinsically low loss material, such as high-quality, single-crystal lightly doped silicon or un-doped silicon. Second, the resonance mode has to have excellent vibration isolation in order to minimize the external energy loss. Both methods have been successful. In particular, highly optimized vibration isolation is designed in and achieved by exemplary embodiments, as will be detailed below. Young's modulus measurements made with the exemplary Young's Modulus Resonator (YMR) embodiments described herein can be combined with shear modulus measurements from a double-paddle oscillator (DPO) to give a complete description of the elastic properties of isotropic thin film materials, including properties such as Poisson's ratio and bulk modulus, via known relations between the elastic constants.
FIG. 1A illustrates a picture of a Young's Modulus Resonator (YMR). FIG. 1B illustrates exemplary dimensions of the YMR in millimeters.
Further, according to R. Djakaria et al. Determination of Young's Modulus of Thin Films used in Embedded Passive Devices; 1997 Electronic Components and Technology Conference; IEEE; O-7803-3857-X/97; pp. 745-749 (1997): “The trends of increasing speed and circuit density in integrated circuits have created demands for new electronic packaging technologies. One technology that meets these demands uses multiple layers of thin film conductors, dielectrics and insulators to form embedded passive devices. One potential application of these embedded devices is the utilization of embedded thin film capacitors to replace surface mount technology (SMT) capacitors. For example, in portable communications devices there are typically more than 20 SMT capacitors . . . . The embedded design thus has a tremendous advantage over the SMT design due to the potential for a more compact package and for a more efficient manufacturing process. The thin films used for embedded passive devices are usually formed by evaporation, sputtering or electrolytical deposition. Under various conditions, these thin film assemblies deform or crack. Such phenomena, which adversely affect circuit performance, cannot be accurately predicted using the mechanical properties of bulk materials. Depending on how the thin film is formed, the mechanical properties are often different from those of the bulk material. To assess accurately the reliability of these thin films the mechanical properties, such as Young's modulus, need to be known . . . . There are several mechanical property measurement techniques which can be used to determine the Young's modulus of a thin film. Three commonly used . . . [measurement] techniques are microindentation, microbeam curvature and mechanical resonant frequency. In the microindenter technique, loads and penetrations of the indenter are continuously measured and recorded. An indentation curve of the load versus depth of penetration obtained from the test is used to determine the Young's modulus of the thin film being tested. One of the disadvantages of this technique is that the thin film being tested must be greater than about 20 micrometers in thickness. A relatively thick film is required so that the unloading microindentation curve enters the linear region as required to determine an elastic recovery value—one of the variables used to calculate the Young's modulus. The Vickers microindenter technique is commonly used for this measurement. In this technique a diamond pyramid indenter is used. The advantage of using the diamond indenter is that the technique can be used to test all materials due to diamond's hardness. A Vickers microindenter machine usually consists of three basic components: a diamond pyramid indenter, a load applying mechanism and an optical system to read the diagonal of the indentation. The diamond pyramid usually has a square base with an angle between its faces of 130-148 degrees. The optical system is usually similar to a regular optical microscope with a resolution of up to a micrometer . . . . In the microbeam curvature deflection technique, a microcantilever beam, with a thin film deposited onto one of its faces, is used to determine the Young's modulus of that thin film . . . [using] simple beam theory . . . by noting the deflection induced by a nano-indenter of a known load. The micro-cantilever beam is usually fabricated by a conventional silicon micromachining technique. The thin film is then deposited onto the prefabricated SiO2 micro-cantilever beam by a sputtering process. Very high resolution equipment is needed to measure the very small dimensions associated with this technique. Typical thickness, width and length dimensions of the beams re 1.0, 20, and 30 micrometers . . . . In the mechanical resonant frequency technique, a micro-cantilever beam with a thin film deposited onto it, or with a stretched circular thin film membrane assembly, is vibrated electrostatically, and the Young's modulus of the thin film is determined from the mechanical resonant frequency of the assembly. A variable-frequency sinusoidal vibrator is applied to the tested assembly, and the movement of the tested assembly is detected by focusing a laser beam on the tested assembly and monitoring the reflected laser beam. The reflected beam is recorded as a function of frequency from which the mechanical resonant frequency can be determined. The mechanical resonant frequency technique is described by Peterson and Guarnieri . . . . The major disadvantages of this technique are the complexity associated with the fabrication of the tested specimen and the complexity of the testing apparatus . . . . The standard tensile test is one of the most common methods used to determine the mechanical properties of a material. The elastic deformation data obtained from this test are used to determine the Young's modulus of the tested material. In this test a specimen is extended under a steadily increasing load, and the external load is applied so that the specimen is in a state of uniaxial stress. Currently, the Young's modulus of the thin films used in the integrated circuits has not been determined by this technique due to the problem associated with separating the thin films from the silicon wafers without deforming them. To overcome this difficulty a flexible polyimide film is utilized as the substrate onto which the thin film is deposited. The polyimide and thin film assembly . . . [are] then used as the specimen of the standard tensile test. This technique . . . [allows] the determination of the thin film knowing the Young's modulus of the polyimide film. The thickness ratio of the thin film and the polyimide film of the tested polyimide-thin film specimen will determine the accuracy of this technique.”
Conventional cantilever devices can measure the elastic properties of thin films (see (see B. S. Berry et al., “Vibrating Reed Internal Friction Apparatus for Films and Foils”, IBM Journal of Research and Development (1975) vol. 19, p. 334; and K. E. Petersen et al., “Young's modulus measurements of thin films using micromechanics, Journal of Applied Physics, (1979) vol. 50, p. 6761); and G. J. McShane, et al. “Young's modulus measurement of thin film materials using micro-cantilevers”. Microengineering (2006) vol. 16, p. 1926). Although efforts have been achieved which make very thin cantilevers (see K. E. Petersen et al., “Young's modulus measurements of thin films using micromechanics, Journal of Applied Physics, (1979) vol. 50, p. 6761); and G. J. McShane, et al. “Young's modulus measurement of thin film materials using micro-cantilevers”, Microengineering (2006) vol. 16, p. 1926), the measurement resolution still suffers from the poor Q of those devices. Techniques have also been developed to remove the substrates in some circumstances and measure the Young's modulus of free standing films (see J. J. Vlassak and W. D. Nix, Journal of Materials Research, “A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films”, (1992), vol. 7, p. 3242). However, as mentioned above, the results may not apply to the film on substrate situation, which is far more common in real-world applications. The technique developed in this work is simple, robust, and reproducible. Most importantly, the finite element modeling design (see FIG. 6A and FIG. 6B) has greatly improved vibration isolation. In comparison to other techniques, exemplary embodiments of YMR exhibit a Q of at least ten times higher (i.e., at least one order of magnitude higher) than conventional techniques and frequency resolution at least one order of magnitude higher.